





from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

__A							   =							TypeVar("T")



class   _SCREAMING_SNAKE_CASE		(      Generic[T]       ):







 '''simple docstring'''

 def __init__(self							:  Optional[Any]			,					UpperCAmelCase_							:  list[T]			,					UpperCAmelCase_							:  Callable[[T, T], T])			->None:



   '''simple docstring'''



   lowerCamelCase__: Any | T         =None

   lowerCamelCase__: int         =len(UpperCAmelCase_)
   lowerCamelCase__: list[T]         =[any_type for _ in range(self.N)] + arr
   lowerCamelCase__: Optional[int]         =fnc
   self.build()

 def 				SCREAMING_SNAKE_CASE_   (self							:  int)			->None:



   '''simple docstring'''



   for p in range(self.N - 1			,					0			,					-1):
     lowerCamelCase__: Union[str, Any]         =self.fn(self.st[p * 2]			,					self.st[p * 2 + 1])

 def 				SCREAMING_SNAKE_CASE_   (self							:  List[Any]			,					UpperCAmelCase_							:  int			,					UpperCAmelCase_							:  T)			->None:



   '''simple docstring'''



   p += self.N
   lowerCamelCase__: Any         =v
   while p > 1:
     lowerCamelCase__: int         =p // 2
     lowerCamelCase__: List[str]         =self.fn(self.st[p * 2]			,					self.st[p * 2 + 1])







 def 				SCREAMING_SNAKE_CASE_   (self							:  int			,					UpperCAmelCase_							:  int			,					UpperCAmelCase_							:  int)			->T | None:  # noqa: E741



   '''simple docstring'''



   lowerCamelCase__    ,   lowerCamelCase__: List[str]         =l + self.N, r + self.N

   lowerCamelCase__: T | None         =None
   while l <= r:
     if l % 2 == 1:
       lowerCamelCase__: Optional[Any]         =self.st[l] if res is None else self.fn(UpperCAmelCase_			,					self.st[l])
     if r % 2 == 0:
       lowerCamelCase__: int         =self.st[r] if res is None else self.fn(UpperCAmelCase_			,					self.st[r])
     lowerCamelCase__    ,   lowerCamelCase__: str         =(l + 1) // 2, (r - 1) // 2
   return res


if __name__ == "__main__":
     from functools import reduce

     __A							   =							[1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]

     __A							   =							{
         0: 7,
         1: 2,
         2: 6,
         3: -14,
         4: 5,
         5: 4,
         6: 7,
         7: -10,
         8: 9,
         9: 10,
         10: 12,
         11: 1,
     }

     __A							   =							SegmentTree(test_array, min)
     __A							   =							SegmentTree(test_array, max)
     __A							   =							SegmentTree(test_array, lambda a, b: a + b)





     def 	lowerCAmelCase_					(			)	->						None:







       """simple docstring"""





       for i in range(len(__a						)						):
         for j in range(__a      ,       len(__a						)						):
           lowerCamelCase__: str         =reduce(__a      ,       test_array[i : j + 1]						)
           lowerCamelCase__: Optional[Any]         =reduce(__a      ,       test_array[i : j + 1]						)
           lowerCamelCase__: Optional[Any]         =reduce(lambda __a      ,       __a						: a + b      ,       test_array[i : j + 1]						)
           assert min_range == min_segment_tree.query(__a      ,       __a						)
           assert max_range == max_segment_tree.query(__a      ,       __a						)
           assert sum_range == sum_segment_tree.query(__a      ,       __a						)

     test_all_segments()

     for index, value in test_updates.items():
          __A							   =							value
          min_segment_tree.update(index, value)
          max_segment_tree.update(index, value)
          sum_segment_tree.update(index, value)
          test_all_segments()






'''simple docstring'''

# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)

@flax.struct.dataclass
class 							a__:
			a_	: CommonSchedulerState

			# setable values
			a_	: jnp.ndarray
			a_	: jnp.ndarray
			a_	: Optional[int]									=      None






			@classmethod
			def 						_lowercase  (     cls					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase						)							->							Dict:
					return cls(common=_UpperCAmelCase					,   init_noise_sigma=_UpperCAmelCase					,   timesteps=_UpperCAmelCase						)





@dataclass
class 							a__( snake_case__     ):
			a_	: DDPMSchedulerState





class 							a__( snake_case__   ,      snake_case__     ):
			a_	: Union[str, Any]									=      [e.name for e in FlaxKarrasDiffusionSchedulers]

			a_	: jnp.dtype






			@property
			def 						_lowercase  (     self						)							->							Union[str, Any]:
					return True






			@register_to_config
			def __init__(     self					,   _UpperCAmelCase = 1000					,   _UpperCAmelCase = 0.0_001					,   _UpperCAmelCase = 0.02					,   _UpperCAmelCase = "linear"					,   _UpperCAmelCase = None					,   _UpperCAmelCase = "fixed_small"					,   _UpperCAmelCase = True					,   _UpperCAmelCase = "epsilon"					,   _UpperCAmelCase = jnp.floataa					,   )							->							Union[str, Any]:
					snake_case__	     =dtype






			def 						_lowercase  (     self					,   _UpperCAmelCase = None						)							->							DDPMSchedulerState:
					if common is None:
							snake_case__	     =CommonSchedulerState.create(self						)

					# standard deviation of the initial noise distribution
					snake_case__	     =jnp.array(1.0					,   dtype=self.dtype						)

					snake_case__	     =jnp.arange(0					,   self.config.num_train_timesteps						).round()[::-1]

					return DDPMSchedulerState.create(
					    common=_UpperCAmelCase					,   init_noise_sigma=_UpperCAmelCase					,   timesteps=_UpperCAmelCase					,   )






			def 						_lowercase  (     self					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase = None						)							->							jnp.ndarray:
					return sample






			def 						_lowercase  (     self					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase = ()						)							->							DDPMSchedulerState:
					snake_case__	     =self.config.num_train_timesteps // num_inference_steps
					# creates integer timesteps by multiplying by ratio
					# rounding to avoid issues when num_inference_step is power of 3
					snake_case__	     =(jnp.arange(0					,   _UpperCAmelCase						) * step_ratio).round()[::-1]

					return state.replace(
					    num_inference_steps=_UpperCAmelCase					,   timesteps=_UpperCAmelCase					,   )






			def 						_lowercase  (     self					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase=None					,   _UpperCAmelCase=None						)							->							Optional[Any]:
					snake_case__	     =state.common.alphas_cumprod[t]
					snake_case__	     =jnp.where(t > 0					,   state.common.alphas_cumprod[t - 1]					,   jnp.array(1.0					,   dtype=self.dtype						)						)

					# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
					# and sample from it to get previous sample
					# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
					snake_case__	     =(1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

					if variance_type is None:
							snake_case__	     =self.config.variance_type

					# hacks - were probably added for training stability
					if variance_type == "fixed_small":
							snake_case__	     =jnp.clip(_UpperCAmelCase					,   a_min=1E-20						)
					# for rl-diffuser https://arxiv.org/abs/2205.09991
					elif variance_type == "fixed_small_log":
							snake_case__	     =jnp.log(jnp.clip(_UpperCAmelCase					,   a_min=1E-20						)						)
					elif variance_type == "fixed_large":
							snake_case__	     =state.common.betas[t]
					elif variance_type == "fixed_large_log":
							# Glide max_log
							snake_case__	     =jnp.log(state.common.betas[t]						)
					elif variance_type == "learned":
							return predicted_variance
					elif variance_type == "learned_range":
							snake_case__	     =variance
							snake_case__	     =state.common.betas[t]
							snake_case__	     =(predicted_variance + 1) / 2
							snake_case__	     =frac * max_log + (1 - frac) * min_log

					return variance






			def 						_lowercase  (     self					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase = None					,   _UpperCAmelCase = True					,   )							->							Union[FlaxDDPMSchedulerOutput, Tuple]:
					snake_case__	     =timestep

					if key is None:
							snake_case__	     =jax.random.PRNGKey(0						)

					if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
							snake_case__     ,	snake_case__	     =jnp.split(_UpperCAmelCase					,   sample.shape[1]					,   axis=1						)
					else:
							snake_case__	     =None

					# 1. compute alphas, betas
					snake_case__	     =state.common.alphas_cumprod[t]
					snake_case__	     =jnp.where(t > 0					,   state.common.alphas_cumprod[t - 1]					,   jnp.array(1.0					,   dtype=self.dtype						)						)
					snake_case__	     =1 - alpha_prod_t
					snake_case__	     =1 - alpha_prod_t_prev

					# 2. compute predicted original sample from predicted noise also called
					# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
					if self.config.prediction_type == "epsilon":
							snake_case__	     =(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
					elif self.config.prediction_type == "sample":
							snake_case__	     =model_output
					elif self.config.prediction_type == "v_prediction":
							snake_case__	     =(alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
					else:
							raise ValueError(
							    f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` """
							    ' for the FlaxDDPMScheduler.'						)

					# 3. Clip "predicted x_0"
					if self.config.clip_sample:
							snake_case__	     =jnp.clip(_UpperCAmelCase					,   -1					,   1						)

					# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
					# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
					snake_case__	     =(alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
					snake_case__	     =state.common.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

					# 5. Compute predicted previous sample µ_t
					# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
					snake_case__	     =pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

					# 6. Add noise
					def random_variance():
							snake_case__	     =jax.random.split(_UpperCAmelCase					,   num=1						)
							snake_case__	     =jax.random.normal(_UpperCAmelCase					,   shape=model_output.shape					,   dtype=self.dtype						)
							return (self._get_variance(_UpperCAmelCase					,   _UpperCAmelCase					,   predicted_variance=_UpperCAmelCase						) ** 0.5) * noise

					snake_case__	     =jnp.where(t > 0					,   random_variance()					,   jnp.zeros(model_output.shape					,   dtype=self.dtype						)						)

					snake_case__	     =pred_prev_sample + variance

					if not return_dict:
							return (pred_prev_sample, state)

					return FlaxDDPMSchedulerOutput(prev_sample=_UpperCAmelCase					,   state=_UpperCAmelCase						)






			def 						_lowercase  (     self					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   )							->							jnp.ndarray:
					return add_noise_common(state.common					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase						)






			def 						_lowercase  (     self					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase					,   )							->							jnp.ndarray:
					return get_velocity_common(state.common					,   _UpperCAmelCase					,   _UpperCAmelCase					,   _UpperCAmelCase						)






			def __len__(     self						)							->							Optional[int]:
					return self.config.num_train_timesteps




